Gravimetric determination of anomalies lateral to boreholes

ABSTRACT

A portable gravimeter is traversed over a selected interval in an exploratory borehole. Formation density data is obtained for the same selected interval. This gravity and density information is then combined with the gravity value at the surface of the borehole when no anomaly is present, the &#39;&#39;&#39;&#39;free air&#39;&#39;&#39;&#39; correction and the Bouguer correction to obtain a measured perturbation effect. The measured perturbation effect represents the net perturbation in the gravity values measured within the borehole due to the presence of a gravimetric anomaly lying lateral to the borehole. The measured perturbation effect is subjected to high pass filtering to render it solely a function of the lateral distance from the borehole to the adjacent flank of the gravimetric anomaly. A trend is subtracted from the filtered measured perturbation effect. Anomaly models are then employed to simulate the gravimetric anomaly which produces the measured perturbation effect. A calculated perturbation effect is generated for the anomaly model. This calculated perturbation effect is high pass filtered and is subjected to trend subtraction. Finally, the filtered measured perturbation effect is compared with the filtered calculated perturbation effect and differences are noted. The parameters of the anomaly model are varied to reduce these differences and further comparisons are made. The process of varying parameters and making comparisons is repeated with the aid of iterative computer programs employing regression techniques such as the method of least squares. When the differences between the filtered measured perturbation effect and the filtered calculated perturbation effect are smaller than some preassigned arbitrary number the anomaly model represents the actual anomaly. The distances between the anomaly model and the simulated borehole are the actual distances between the gravimetric anomaly and the exploratory borehole.

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"hi -73 as United States Patent Yungul 1 July 24, 1973 GRAVIMETRICDETERMINATION OF ANOMALIES LATERAL TO BOREHOLES Snlhi H. Yungul,Fullerton, Calif.

[73] Assignee: Chevron Research Company, San

Francisco, Calif.

[22] Filed: July 27, 1970 [21] Appl. No.: 59,783

[75] inventor:

Primary Examiner-Jerry W. Myracle Att0rney-R. L. Freeland, J. A.Buchanan, Jr. and G. F. Magdeburger 57 ABSTRACT A portable gravimeter istraversed over a selected interval in an exploratory borehole. Formationdensity data is obtained for the same selected interval. This gravityand density information is then combined with the gravity value at thesurface of the borehole when no anomaly is present, the free air"correction and the Bougucr correction to obtain a measured perturbationeffect. The measured perturbation effect represents the net perturbationin the gravity values measured within the borehole due to the presenceof a gravirnetric anomaly lying lateral to the borehole. The measuredperturbation effect is subjected to high pass filtering to render itsolely a function of the lateral distance from the borehole to theadjacent flank of the gravimetric anomaly. A trend is subtracted fromthe filtered measured perturbation effect. Anomaly models are thenemployed to simulate the gravimetric anomaly which produces the measuredperturbation effect. A calculated perturbation effect is generated forthe anomaly model. This calculated perturbation effect is high passfiltered and is subjected to trend subtraction. Finally, the filteredmeasured perturbation effect is compared with the filtered calculatedperturbation effect and differences are noted. The parameters of theanomaly model are varied to reduce these differences and furthercomparisons are made. The process of varying parameters and makingcomparisons is repeated with the aid of iterative computer programsemploying regression techniques such as the method of least squares.When the differences between the filtered measured perturbation effectand the filtered calculated perturbation effect are smaller than somepreassigned arbitrary number the anomaly model represents the actualanomaly. The distances between the anomaly model and the simulatedborehole are the actual distances between the gravimetric anomaly andthe exploratory borehole.

8 Claims, 10 Drawing Figures Pmmwm V 3.747.403

SHEET 1 UP 4 INVENTOR SULH/ H. VU/VGUL PATENIEDJULZMQH SHEET 2 (IF 4INVENTOR SULH/ H. VUNGUL T c N B HH. TCA N GRAVIMETRIC DETERMINATION OFANOMALIES LATERAL T BOREI-IOLES The present invention relates to gravityprospecting. More particularly, it relates to determining (l thedistance to the flanks of a salt dome from a wellbore drilled throughearth formations adjacent to said salt dome, (2) the distance to a rockformation in the proximity of a wellbore that has been near-missed bythe well, and (3) the boundaries of a salt dome or rock formation thathas been penetrated by the well.

BRIEF DESCRIPTION OF THE DRAWINGS For assistance in obtaining a moredetailed understanding of the method of my invention, reference may behad to the following description of the drawings which are incorporatedherein and made a part of this specification.

FIG. I is a pictorial diagram of an irregular salt dome which hasintruded into a sedimentary formation. An exploratory wellbore is shownas penetrating the top of the salt dome at one point and as extendingalongside the dome elsewhere.

FIG. 2a is a pictorial diagram of an exploratory wellbore drilled in asedimentary formation in a region where no anomalies are present.

FIG. 2b is a pictorial diagram of an exploratory wellbore drilled in asedimentary formation in the vicinity of a salt dome.

FIG. 3 is a stack of discs with varying radii and thicknesses whichrepresents, in one embodiment of my invention, the unknown anomaly on anautomated data processing machine such as a digital computer.

FIG. 4 is a stack of semi-infinite horizontal slabs which represent, inanother embodiment of my invention, the unknown anomaly on an automateddata processing machine such as a digital computer.

FIG. 5a is a graph illustrating the measured perturbation effect.

FIG. 5b is a graph illustrating the measured gradient derived from themeasured perturbation effect of FIG. 50.

FIG. 5c is a graph illustrating the measured layer signature derivedfrom the measured gradient of FIG. 511.

FIG. 5d is a graph illustrating the fit obtained between the measuredlayer signature of FIG. 50 and the computed layer signature derived fromthe anomaly representation of FIG. 4.

FIG. Se is a pictorial diagram illustrating the salt flank profileobtained by employing the FIG. 4 embodiment of my invention.

GENERAL BACKGROUND OF THE INVENTION An appreciable portion of the oilproduction in the United States is from reservoirs associated withpiercement salt domes in the Gulf of Mexico region and in the ParadoxBasin. About twelve percent of the domestic production in l964 came fromsalt dome structures of all types. Most of the oil associated withpiercement domes is found within 1,000 feet of a salt flank in themanner shown in FIG. 1. The general location of the salt dome is knownfrom surface exploration, but the locations of its flanks, especially atcertain depths where possible pay sands may be truncated by the salt,are not known with an accuracy that would be sufficient for oil fielddevelopment. Referring now to FIG. 1, one can see that Oil A wasdiscovered to be associated with Sand A, while Sand B turned out to bedry. If the salt flank is only a few hundred feet away from thewellbore, it is very likely that this sand is dry throughout. However,if the flank is far away, say 1,200 feet away, Sand B could have an oilpool near the flank and should be explored by a properly deflectedborehole that has to be planned in accordance with the location of thesalt flank at the depth of Sand B. Therefore, knowledge of the saltflank configuration is of critical economic importance. At present, saltflanks are developed to some extent by trial-and-error drilling, whichis expensive. If a borehole does not hit an expected producing zone, itbecomes very important to measure the distance, x, from the borehole tothe salt flank as a function of depth, 2, as shown in FIG. 1.

Previous methods of solution to the general problem indicated above havebeen given in three U.S. Patents. U.S. Pat. No. 3,256,480, issued toRunge, Worthington and Yungul, teaches a method in which the signalsfrom long-spaced electric logging tools, tools whose electrodes arespaced apart at distances of feet or more, are compared with those fromshort-spaced electric logging tools to detect the resistivity effects ofanomalous bodies lateral to the borehole. U.S. Pat. Nos. 3,286,168 and3,412,815, both issued to I-Iolser, Unterberger, and Jones, teach themethod of reflecting electromagnetic radiation from the walls of a saltdome to determine the distance to those walls, the radiation being sentfrom and received by an instrument within a borehole drilled inside thesalt dome. Each of these prior art methods has its particularusefulness, but it also has particular requirements in order that it maybe carried out. For instance, the electrical method of Runge,Worthington and Yungul definitely requires an uncased borehole outsidethe anomaly, e.g., the salt dome to be detected, while the method ofHolser, Unterberger and Jones definitely requires an uncased boreholeinside the salt dome whose walls are to be delineated. In the method ofmy invention, any type of borehole is suitable, cased or uncased, insideor outside, or partly inside and partly outside the anomalous body, andthe type of borehole drilling fluid, or lack or it, does not appreciablyaffect the practice of the method of my invention.

In FIG. 2a the geologic formations in the region of the wellbore areshown to be horizontal layers of inflnite extent. Thus, the densityfunction, a, is a function of depth, 2, only. The gravity measured atthe surface, at zero depth, is denoted by g(0), and the gravity at adepth, z, is denoted by g(z). It is well known in the art of gravityprospecting that g'(z) is related to g'(0) via the free-air" and Bouguercorrections in a fixed manner:

where F is the normal (non-anomalous) vertical gradient of the earthsgravitational field in the air (also called the free-air gradient) and'y is the universal gravitational constant. In the right hand expressionof equation (1), the second term is called the free-air correction andthe third term is called the Bouguer correction. These corrections, aswell as the magnitudes of F and 'y are discussed and defined inreference textbooks on gravitational exploration. See, for example,Grant and West, Interpretation Theory in Applied Geophysics, Chapter 9,1965.

In FIG. 2b equation (1) is not valid due to the fact that the subsurfaceno longer has horizontal homogeneity. In this case the gravity at thesurface is denoted by g(()) and the gravity at depth 2 is denoted byg(z). The value of g(z), however, can be related to that of g'(z) byconsidering g(z) to be the result of a horizontally layered subsurface,i.e., g'(z), plus a perturbation effect, G(z). The perturbation effectis due to the fact that some of the sedimentary section of density hasbeen replaced by salt of density 0,. From this statement it follows thatthe perturbation log is given by:

Since gravity measurements are relative, the constant g(0) can beassumed to be zero or any arbitrary but convenient number. Theperturbation effect is seen to be the anomalous gravitational effect dueto a fictitious mass distribution confined to the volume of the salt;the density of the fictitious mass distribution is 8(1) 0-,, 0(2) and iscalled the density contrast. As far as the perturbation effect, G(z), isconcerned, no mass exists outside the volume taken up by the anomaly.The perturbation effect, then, is dependent solely on anomalous bodieslateral to the borehole.

It would seem that the measured perturbation effect could be used in astraightforward manner to determine salt geometry. This straightforwardapproach involves taking a surface gravity map consisting of g(0) valuesat a plurality of geographic positions on the earths surface andinterpreting the map with the use of the known values of o'(z) and 0,.The interpretation is intrinsically ambiguous because an infinite numberof possible salt dome configurations could have been responsible for thesurface gravity map. However, only one of the possible salt domeconfigurations would have yielded a perturbation log identical to themeasured log of the perturbation effect. Thus, the measured log of theperturbation effect could be used to determine the salt geometry.However, this method, although simple, is not practical; its accuracy isinadequate and the cost of conducting such an analysis is high. Thereare three reasons for the impraeticality. First, surface gravity is notsensitive to structure over a steep flank at appreciable depths, such asthe undulations near Oil "8 in FIG. 1. Second, the perturbation log isseverely truncated. For example, in FIG. 1, data is available onlywithin the depth range between z, and z, while an adequate definition ofthe salt mass would require data from a range four times as large,including data for heights in the air and data for depths under thesalt. Third, the fitting process necessary to obtain a fit betweenmeasured and computed perturbation logs is very laborious because thesalt surface is threedimensional, large, and complex, and the process,

therefore, does not lend itself to an automatic selfiterative operationthat can be done by means of electronic computers.

The object of my invention, then, is to determine the distance, x, tothe salt flank as a function of depth, z. directly from a log of theperturbation effect which has been measured within the 12 z, intervalonly, as shown in FIG. ll, without relying on a surface gravity map andsalt models derived therefrom.

It is also an object of my invention to render the determination of thedistance, x, to the salt flank effectively independent of the distantzone of the salt surface, i.e., that portion of the salt which liesrelatively far from the logged part of the wellbore. The distant zone isrepresented in FIG. 1 by a dashed line. This latter objective istheoretically impossible to achieve exactly but if some amount oftheoretical error, in addition to experimental error, is allowed, thenit becomes possible and practical to achieve this objective.

BRIEF DESCRIPTION OF THE INVENTION To accomplish the aforementionedobjectives, the measured log of the perturbation effect, G(z), isanalogized to a time-series, where 1 represents the time, so that theapplication of filtering to G(z) can be stated in familiar terminology,e.g., frequencyfin terms of cycles per unit length of Then, inaccordance with the well known theory of gravitational potential, theattenuation of a harmonic component of frequency,f, of the G(z) functionwith distance, d, from the source of gravitational attraction (theanomalous mass) to a point of observation in the wellbore isproportional to the factor [exp.(27rfd)]. Consequently, the contributionof the distant zone to the G(z) function resides primarily in the lowfrequencies, the high frequencies having been effectively attenuated dueto the relatively large distance. Therefore, the effect of the distantzone can be made tolerable if an appropriate kind of high-pass filteringof the G(z) is done. The result of appropriate filtering is that thefiltered G(z) function, excluding those portions near either end of themeasured log of the perturbation effect, depends on the one unknownparameter, x, namely the distance to the salt. The relatively highfrequency variations in the filtered G(z) function are practicallysolely due to the truncation of sedimentary formations against the saltflank in juxtaposition to the wellbore in the region ofinquiry and arehereinafter called layer signatures. Since x is the only independentparameter, it can be obtained by running a selfiterating automaticfitting program on an automated data processing machine whereby x isvaried until a computed layer signature is matched to the measured layersignature. The x distances corresponding to the layer signature whichmatches the measured log of the perturbation effect represent, in fact,the actual lateral distances from the wellbore to the flanks of the saltdome. Of course, since the selection of layer signatures is generated byfiltering a series of hypothetical logs of perturbation effects, it isnecessary to filter the hypothetical logs of the perturbation effect inthe same manner as the logs of the measured perturbation effect arefiltered in order to preserve a quantitative correspondence between thecomputed and measured layer signatures.

DETAILED DESCRIPTION OF THE INVENTION While the previous description ofmy invention is generally adequate, a more detailed understanding of theindividual steps which comprise the method of my invention can beobtained by reference to the following sequential listing of steps.

1. Run a borehole gravimeter in a wellbore to obtain g(z), gravity as afunction of depth.

2. Run a density logging tool such as a gammagamma densilogger in awellbore, or measure the density of core samples taken at various depthsin a wellbore, or compute the density from a set of other types of logs,or compute the density in a wellbore via equation (1) from gravimetricmeasurements made in another wellbore which is substantially far fromany lateral inhomogeneity, and thereby obtain the formationdensity-versus-depth function, o(z).

3. Obtain the perturbation log, G(z), by inserting the measured valuesfor g(z) and 0(z) in equation (2).

4. Perform a high-pass filtering operation of the perturbation log,G(z), e.g., take the vertical gradient of G(z) or derivatives of higherorder. In one embodiment of my invention a vertical gradient of gravityis measured directly thereby permitting the direct derivation of thefirst derivative of the perturbation log, G'(z).

5. Subtract a trend, T(z), from the filtered G(z). T(z) may be obtainedby fitting a polynomial of low degree to the perturbation effect, G(z),by using an automatic, weighted least-squares fitting program on adigital computer. Removal of trends from measured data by polynomialfitting using the method of least-squares is well known in the art. See,for instance, A Problem in the Analysis of Geophysical Data," by F.Grant in Geophysics, 22, 309-344 (1957). The trend which is subtractedis not necessarily monotonic and may have a polynominal character whichreflects the character of the filtered perturbation effect, G(z). Thedegree of T(z), i.e., the degree of the polynomial used to fit theperturbation effect, G(z), is obtained automatically by a subroutineincluded in the automatic fitting program. The degree of the polynomialcan be selected automatically in a subroutine by successively increasingit until the improvement in the fit of the polynomial to G(z) is smallerthan some prescribed value. In practice, the degree may vary from 3 tobut is usually not greater than 5. Alternatively, the degree may beobtained by a visual inspection of the filtered perturbation effect,0(2)- The trend can also be obtained by utilizing spline fittingtechniques. These techniques involve fitting a function which is apolynomial over subintervals, to the perturbation effect, G(z).

The result of the subtraction of the trend is denoted as the measuredlayer signature, D(z). The trend subtraction step can be interchangedwith Step 4 but it cannot be eliminated because the length of the timeseries" otherwise would be too short for the wavelengths associated withthe distant portions of anomalies so that statistical time-seriesanalysis could not be used to isolate the layer signatures.

6. Employ an anomaly model type, previously programmed on a digitalcomputer, to simulate the presence of an anomaly. In one embodiment ofmy invention the programmed model type is the stack of horizontalco-axial (the axis is parallel to the borehole) discs with varying radiiand thicknesses shown in FIG. 3. The distance, L, shown in FIG. 3 can beestimated from other data but the estimate need not be accurate. Inanother embodiment a stack of horizontal slabs is used. These slabs areoriented so that the borehole is located on the common median plane ofthe rectangles, the three sides of the rectangular slabs farthest awayfrom the boreholes lie on common vertical planes and so that the sidesopposite to the borehole are step-wise. In a still further embodiment astack of horizontal semiinfinite slabs is used as shown in FIG. 4. Theseslabs are identical to the rectangular slabs described above except thatthe sides of the slabs most remote from the borehole are assumed to beat infinity. This assumption simplifies computation and introduceslittle error so long as the average ratio of the radius of the anomalousmass being investigated to the distance between the borehole and theanomalous mass, x, is larger than about 4. The average diameter ofpiercement salt domes in the Gulf Coast region in the United States isabout 2 miles so that the semi-infinite slab is a suitable embodimentwhen my invention is practiced with data taken in the vicinity of GulfCoast salt domes. In general, any programmed anomaly model type can beused so long as x, the distance between the borehole and the anomaly, isthe only independent variable.

When a region is known to have a dip an anomaly model can be programmedso that the layers of rock which surround the model are assigned theknown dip. The introduction of a dip renders the practice of the methodof my invention more difficult. The examples relied upon, therefore, insubsequent steps will be based on the case of horizontal layering.

Beyond this point no human intervention is required; an electroniccomputer completes the solution by means of a regression method computerprogram and lists or plots the distances, x, for each layer, from theborehole to the salt flank. The initial distances can be pickedarbitrarily by the computer program, but an initial realistic estimatemay reduce computation time. The algorithm employed by the computer isexplained in the following steps.

7. Compute automatically by means of a digital computer thegravitational effect that the simulated anomaly would have at aplurality of points along the borehole, a computation which is wellknown in the art of gravity exploration. See, for example, Grant andWest, Interpretation Theory in Applied Geophysics, Chapter 10, 1965.This gravitational effect is called the computed perturbation log and isdesignated G(z). In reality, G(z) is the vertical component of thegravitational attraction due to the aforementioned model type whichconsists of layers of thickness 1, and the fictitious density, 8,, allconfined to the volume of the anomalous mass (e.g., salt). The values oft, and 8, are known from Step 2.

8. Perform the same high-pass filtering operation on the computedperturbation effect, G(z), as was performed on the perturbation, G(z),in Step 4.

9. Remove a "trend, T(z) from the filtered G(z). T(z) need not be thesame as T(z) which was used in Step 5, but may be generated in any ofthe ways discussed therein. As above, the trend need not be monotonicand its character will reflect the character of the filtered computedperturbation effect. The order of Steps 8 and 9 may be reversed. Theresult of Step 9 is designated as the computed layer signature, 5(2).

10. The measured layer signature, D(z), is known at a plurality ofobservation points, z,, where j 1,2,3,

m. These values are represented by D,(z,). The computed layer signature,(z), is computed for all of the observation points, it is a function ofthe observation point depth, 1,, the layer thickness, t,, where i=l,2,3, n, and n is the number of layers in the anomaly model type, thedensity contrasts of the layers, 8,, and the distances, x,,

The quantities 2,, t4, and 8, are known while the x, s are unknown. Theobjective is to vary x, until the inequality DJ E, g E,

is satisfied at all of the observation points, z, (e is an arbitrarilyfixed small quantity). This can be accomplished by employing the wellknown method of leastsquares. The least squares method takes thequantity Q=v2 i i- 11x01 4.

wherej= 1,2,3, .m, andi= 1,2,3, n, and minimizes Q by imposing theconstraints A simultaneous solution of equations (5) would lead to thedetermination of the distances, x,, but since the equations arenon-linear there is no known direct (onestep) process for solving them.Consequently, an iterative procedure requiring linearization of themathematical expressions at some stage must be used. Such linearizationand iteration can be done by the well known Gauss-Newton orNewton-Raphson methods. (See, for instance, R. E. Barieu and B. J.Dalton, Nonlinear Regression and the Principle of Least Squares, U.S.Department of Interior, Bureau of Mines, Report of Investigation 6900,July 1966.) An example of the application of the least-squares method toa similar problem is given by C. E. Corbato in A Least-Squares Procedurefor Gravity Interpretation," Geophysics, 30, 228-233 (1965). Otherregression techniques than the leastsquares method may also be used. Anexample is given by J. H. Healy and F. Press in Geophysical Studies ofBasin Structures Along the Eastern Front of the Sierra Nevada,California, Geophysics, 20, 337-359 (1964).

The distances, x obtained by means of these automatic regressionprocesses, satisfy equation (3) and reveal the vertical profile of theanomalous mass being investigated.

While the foregoing step-wise listing of the elements of my invention issufficient to enable one skilled in the art of gravity exploration topractice my invention, the following example is a typical embodimentwhich demonstrates the utility of my invention.

FIG. 5a is a perturbation log, G(z), calculated by equation (2), supra,from a hypothetical but realistic representation of gravity and densitydata which would ordinarily be determined in accordance with Steps 1 and2. The vertical gradient, AG(z)/Az, of this perturbation log was thentaken and is shown in FIG. Sb. The curve of FIG. 5b, then, representsthe result of highpass filtering and corresponds to the output of Step4, supra.

A trend, T(z), was obtained by fitting a selectively weighted polynomialto the vertical gradient of FIG. 4b. The trend, T(z), was thensubtracted from AG(z)/Az to produce the layer signature, D(z), as shownin FIG. 5c.

The semi-infinite horizontal slab anomaly model consisting of a stack ofhorizontal semi-infinite layers with known thicknesses and densitycontrasts was used to generate a computed perturbation effect C(z). Thevertical gradient of the computed perturbation effect,

6 G (z)/ az, was then taken. A trend, T(z), was then subtracted from 6G(z)/ az in accordance with Step 9, supra, to produce a computed layersignature, D(z).

Finally, the arbitrary x distances between the borehole and thesemi-infinite horizontal layers of the model were varied by aself-iterative program on a digital computer to render the differencesbetween D(z) and 5(2) quite small, as shown in FIG. 5d. The x distancesused to generate the computed layer signatures of the semi-infinitehorizontal slab anomaly model, shown in FIG. 5d, correspond to theactual lateral distances from the borehole to the anomalous body beinginvestigated, as shown in FIG. 52.

The utility of my invention extends to situations other than theinvestigation of the boundaries of gross anomalies. For example, themethod of my invention would apply to determine the proximity of asingle bed of sand which was not intercepted by the wellbore. This issimply the case where the anomaly model would be reduced to a singledisc or slab. Also, the method of my invention can be used to determinethe horizontal extent of a sand bed that has been intercepted by awellbore. The absence of sand beyond the edge of the sand bed is agravitational anomaly whether the surrounding formation is denser orless dense than the sand bed. Finally, if the contour of an anomaly isconvoluted so that an overhang obscures the primary curvature of theanomaly the method of my invention can be used to map the overhang. Amultivariable anomaly model would be required but the method of myinvention would be applied without significant alteration.

While specific examples have been utilized in this specification todemonstrate the method of my invention, it is intended that the scope ofmy invention be limited only by the scope and spirit of the appendedclaims.

I claim:

1. The method of gravimetrically prospecting for geologically anomalousbodies lateral to an exploratory borehole and for determining thelateral distance thereto, comprising the steps of:

a. measuring the density of the formations surrounding said borehole byrunning a gamma-gamma density logging device within said wellbore overthe interval under study;

b. traversing a borehole gravimeter within said wellbore over saidinterval under study to obtain measurements of the acceleration due togravity as a function of depth;

c. determining the net gravitational perturbation effect of ageologically anomalous body in accordance with the followingrelationship:

where g(z) is the acceleration due to gravity as a function of depthwhen an anomaly is present,

- g'(()) is the acceleration due to gravity at the surface when noanomaly is present,

F is the free-air gradient,

7 is the universal gravitational constant, and

(7(1) is the density of the formations as a function of depth;

d. removing the contributions to the net perturbation effect from themore distant regions of said anomaly by taking the vertical gradient orderivatives of higher order of said net perturbation effect therebyrendering said net perturbation effect a function of the singleparameter of lateral distance from said borehole to said anomaly;

e. determining the lateral distances from said borehole to said anomalyat various depths within said interval under study by means of aleast-squares method self-iterating computer program.

2. The method of gravimetrically prospecting for geologically anomalousbodies lateral to an exploratory borehole and for determining theirlateral distances from said borehole over a given depth interval,comprising the steps of:

a. measuring the densities of the geologic formations surrounding saidborehole at a plurality of successive points along said borehole oversaid given depth interval;

b. computing a space-derivative of the gravitational potential thatwould exist over said given interval of said borehole if said measureddensities represented geologic formations that extended laterally awayfrom said borehole to infinity, with no interruptions by lateralanomalous bodies, the first order space-derivative of said gravitationalpotential being represented by the following equation, with higher orderspace-derivatives being derivatives of said equation:

where g'(z) is the acceleration due to gravity as a function of depthwhen no anomaly is present,

g'(0) is the acceleration due to gravity at the surface when no anomalyis present, F is the free-air gradient, 'y is the universalgravitational constant, 0(2) is the density of the formations as afunction of depth, and z is depth;

0. traversing a gravity-responsive instrument along said borehole oversaid given depth interval to measure the corresponding actualspace-derivative of gravitational potential as a function of depth;

d. subtracting said computed space derivative of gravitational potentialfrom said measured actual space-derivative of gravitational potentialfor successive points along said given depth interval, to generate theperturbation function which is due to lateral anomalous bodies;

e. high-pass filtering said generated perturbation function to removethe contributions to said function made by the more distant regions ofsaid lateral anomalous bodies, to produce a filtered perturbationfunction over said depth interval that is dependent mainly upon theshort lateral distances from the said borehole to said anomaly; and f.comparing said filtered perturbation function with a set ofcorresponding filtering perturbation func- 5 tions based on models ofanomalous bodies of various shapes at various distances calculated inaccordance with steps (b) through (e), and choosing the model whosecalculated corresponding filtered perturbation function most nearlymatches said filtered perturbation function derived from steps (a)through (e) as most nearly representing actual anomalous bodies lateralto said borehole, the distances represented in said model beingapproximately the actual distances from said borehole to said actualanomalous bodies.

3. The method of claim 2, wherein said gravityresponsive instrument is aborehole gravimeter which measures the acceleration due to gravity.

4. The method of claim 2, wherein said gravityresponsive instrumentmeasures a space-derivative of gravitational acceleration thereof.

5. The method of claim 2, wherein the densities of said geologicformation are measured in core samples removed from said formations.

6. The method of claim 2, wherein the densities of said formation aremeasured by a density logging device traversed through said borehole.

7. The method of gravimetrically prospecting for geologically anomalousbodies lateral to an exploratory borehole and for determining theirlateral distances from said borehole over a given depth intervalcompris- 30 ing the steps of:

a. measuring the densities of the geologic formations surrounding saidborehole at a plurality of successive points over said given depthinterval;

b. traversing a borehole gravimeter within said borehole over said givendepth interval to measure the acceleration due to gravity as a functionof depth; c. determining the net gravitational perturbation effect of ageologically anomalous body in accordance with the followingrelationship:

v m z where g(z) is the acceleration due to gravity as a function ofdepth when an anomaly is present,

g'(0) is the acceleration due to gravity at the surface when no anomalyis present, F is the free-air gradient, 7 is the universal gravitationalconstant, and o-(z) is the density of the formations as a function ofdepth;

d. removing the contributions to the gravitational perturbation effectfrom the more distant regions of said anomaly by determining aderivative of the gravitational acceleration of said perturbationeffect,

e. subtracting a selectively weighted polynomial function of saidderivative of gravitational acceleration from said net perturbation sothat the remainder of said perturbation effect essentially is a functionof the single parameter of the shortest lateral distance from saidborehole to said anomaly; and

f. determining the shortest lateral distances from said borehole to saidanomaly at various depths within said given depth interval by means of aleastsquares method self-iterating computer program.

8. The method of claim 7 wherein said gravitational 65 accelerationderivative of said net perturbation effect is directly measured as afunction of depth over said given depth interval by means of a gravitygradiometer. 4 i l '8

1. The method of gravimetrically prospecting for geologically anomalousbodies lateral to an exploratory borehole and for determining thelateral distance thereto, comprising the steps of: a. measuring thedensity of the formations surrounding said borehole by running agamma-gamma density logging device within said wellbore over theinterval under study; b. traversing a borehole gravimeter within saidwellbore over said interval under study to obtain measurements of theacceleration due to gravity as a function of depth; c. determining thenet gravitational perturbation effect of a geologically anomalous bodyin accordance with the following relationship:
 2. The method ofgravimetrically prospecting for geologically anomalous bodies lateral toan exploratory borehole and for determining their lateral distances fromsaid borehole over a given depth interval, comprising the steps of: a.measuring the densities of the geologic formations surrounding saidborehole at a plurality of successive points along said borehole oversaid given depth interval; b. computing a space-derivative of thegravitational potential that would exist over said given interval ofsaid borehole if said mEasured densities represented geologic formationsthat extended laterally away from said borehole to infinity, with nointerruptions by lateral anomalous bodies, the first orderspace-derivative of said gravitational potential being represented bythe following equation, with higher order space-derivatives beingderivatives of said equation:
 3. The method of claim 2, wherein saidgravity-responsive instrument is a borehole gravimeter which measuresthe acceleration due to gravity.
 4. The method of claim 2, wherein saidgravity-responsive instrument measures a space-derivative ofgravitational acceleration thereof.
 5. The method of claim 2, whereinthe densities of said geologic formation are measured in core samplesremoved from said formations.
 6. The method of claim 2, wherein thedensities of said formation are measured by a density logging devicetraversed through said borehole.
 7. The method of gravimetricallyprospecting for geologically anomalous bodies lateral to an exploratoryborehole and for determining their lateral distances from said boreholeover a given depth interval comprising the steps of: a. measuring thedensities of the geologic formations surrounding said borehole at aplurality of successive points over said given depth interval; b.traversing a borehole gravimeter within said borehole over said givendepth interval to measure the acceleration due to gravity as a functionof depth; c. determining the net gravitational perturbation effect of ageologically anomalous body in accordance with the followingrelationship:
 8. The method of claim 7 wherein said gravitationalacceleration derivative of said net perturbation effect is directlymeasured as a function of depth over said given depth interval by meansof a gravity gradiometer.